统计研究

指标之间的高度相关性及其重要性差异导致了传统聚类分析方法往往无法获得良好的分类效果。本文在对传统聚类分析方法及其改进方法的局限性展开探讨的基础上,运用数学方法重构了分类定义中的距离概念,通过定义自适应赋权的主成分距离为分类统计量,提出一种新的改进的主成分聚类分析方法——加权主成分距离聚类分析法。理论研究表明,加权主成分距离聚类分析法系统集成了已有聚类分析方法的优点,有充分的理论基础保证其科学合理性。仿真实验结果显示,加权主成分距离聚类分析法能够有效解决已有聚类分析方法在特定情形下的失真问题,所得分类效果更为理想。

Traditional clustering analysis method is often unable to obtain the good classification result because of correlations among indexes and difference in indexes ' importance. This paper discusses the limitations of traditional clustering analysis method and the various improved methods,and reconstructs the concept of distance in classification by using the mathematical methods. Through defining the principal component distance of objective weighting as the classification statistic,it puts forward a new improved principal component clustering analysis method——the clustering analysis method of weighted principal component distance. Theoretical study shows that the new method is scientific rational and integrates the advantages of existing methods. The simulation result shows that the new method can effectively solve the problem of the failure of the existing clustering analysis methods in the specific circumstances,and has satisfactory classification effect.